If x a + x b = x c + x d how do a , b , c , d relationship are?For instance: 3 ( 3 x 2 + 8 ) + 3 ( 4 x + 2 ) = 3 0 + 3 ( 5 x 2 + 7 ) and ( 3 x 2 + 8 ) ( 4 x + 2 ) ≠ 0

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If       x    a    +      x    b    =      x    c    +      x    d   how do   a  ,  b  ,  c  ,  d relationship are?For instance:      3          (      3              x        2            +      8      )        +      3          (      4      x      +      2      )        =      3    0    +      3          (      5              x        2            +      7      )      and  (  3      x    2    +  8  )  (  4  x  +  2  )  ≠  0

cegukwt · Accepted Answer

Let   a  &amp;lt;=  b and   c  &amp;lt;=  d; then we write      x    b    (      x          a      −      b        −  1  )  =      x    d    (      x          c      −      d        −  1  )Also   (  x  ,      x          a      −      b        −  1  )  =  1 and   (  x  ,      x          c      −      d        −  1  )  =  1.       x    b        |        x    b    (      x          a      −      b        −  1  ) than we can say that       x    b        |        x    d    (      x          c      −      d        −  1  ) and       x    b        |        x    d  .The same way we can prove that       x    d        |        x    b  . Than we get that   b  =  d. So we get      x    b    (      x          a      −      b        −  1  )  =      x    b    (      x          c      −      d        −  1  )      x          a      −      b        −  1  =      x          c      −      d        −  1From this equation we can write   a  −  b  =  c  −  d.Using that   b  =  d we have that   a  =  c.

If x^a+x^b=x^c+x^d how do a,b,c,d relationship are? For instance: 3^(3x^2+8)+3^(4x+2)=3^0+3^(5x2+7) and (3x^2+8)(4x+2)≠0

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